Finite Group Databasebeta

← C61×#17272 #29520705

Subgroups — C61×#17272 #29520705

Order 15616.

1426 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#1443C212yesmaximal, complemented
2C61×#1441C212yesmaximal, complemented
3C61×#1439C212yesmaximal, complemented
4C61×#1439C212yesmaximal, complemented
5C61×#1439C212yesmaximal, complemented
6C61×#1439C212yesmaximal, complemented
7C61×#1438C211yesmaximal, characteristic
8C61×#1438C211yesmaximal, characteristic
9C61×#1438C211yesmaximal, characteristic
10C23×D4×C61C2211yescharacteristic
11C22×C4⋊C4×C61C2212yes—
12C22×C4⋊C4×C61C2212yes—
13C22×C22⋊C4×C61C2211yescharacteristic
14C22×C22⋊C4×C61C2212yes—
15C22×C22⋊C4×C61C2212yes—
16C22×C22⋊C4×C61C2212yes—
17C22×C22⋊C4×C61C2211yescharacteristic
18C22×C22⋊C4×C61C2212yes—
19C22×C22⋊C4×C61C2211yescharacteristic
20C22×C22⋊C4×C61C2211yescharacteristic
21C2×#95×C61C2212yes—
22C2×#95×C61C2211yescharacteristic
23C2×#95×C61C2212yes—
24C2×#95×C61C2212yes—
25C2×#95×C61C2211yescharacteristic
26C2×#95×C61C2212yes—
27C2×#95×C61C2212yes—
28C2×#95×C61C2212yes—
29C2×#95×C61C2212yes—
30C2×#95×C61C2212yes—
31C25×C61C2311yescharacteristic
32C25×C61C2311yescharacteristic
33C22×D4×C61—41no—
34C22×D4×C61—42no—
35C22×D4×C61—42no—
36C22×D4×C61—41no—
37C22×D4×C61Q814yes—
38C23×C4×C61C2312yes—
39C23×C4×C61C2312yes—
40C23×C4×C61C2312yes—
41C23×C4×C61C2312yes—
42C23×C4×C61C2311yescharacteristic
43C23×C4×C61C2312yes—
44C23×C4×C61C2312yes—
45C2×C4⋊C4×C61—24no—
46C2×C4⋊C4×C61—42no—
47C2×C4⋊C4×C61—42no—
48C2×C4⋊C4×C61—42no—
49C2×C4⋊C4×C61—42no—
50C2×C4⋊C4×C61—42no—
51C2×C22⋊C4×C61—24no—
52C2×C22⋊C4×C61—24no—
53C2×C22⋊C4×C61—24no—
54C2×C22⋊C4×C61—24no—
55C2×C22⋊C4×C61—41no—
56C2×C22⋊C4×C61—42no—
57C2×C22⋊C4×C61—42no—
58C2×C22⋊C4×C61—42no—
59C2×C22⋊C4×C61—42no—
60C2×C22⋊C4×C61—42no—
61C2×C22⋊C4×C61—42no—
62C2×C22⋊C4×C61—42no—
63C2×C22⋊C4×C61—41no—
64C2×C22⋊C4×C61—41no—
65C2×C22⋊C4×C61—42no—
66C2×C22⋊C4×C61—42no—
67C2×C22⋊C4×C61—42no—
68C2×C22⋊C4×C61—42no—
69C2×C22⋊C4×C61—42no—
70C2×C22⋊C4×C61—41no—
71#95×C61—24no—
72#95×C61—42no—
73#95×C61—42no—
74#95×C61—42no—
75#95×C61—42no—
76#95×C61—41no—
77#95×C61—41no—
78#95×C61—42no—
79#95×C61—42no—
80#95×C61—42no—
81C24×C61—22no—
82C24×C61—22no—
83C24×C61—22no—
84C24×C61—22no—
85C24×C61—22no—
86C24×C61—22no—
87C24×C61—22no—
88C24×C61—22no—
89C24×C61—22no—
90C24×C61—22no—
91C24×C61—22no—
92C24×C61—21no—
93C24×C61—21no—
94C24×C61—22no—
95C24×C61—21no—
96C24×C61—21no—
97C24×C61C2×Q812yes—
98C24×C61C2×Q812yes—
99C24×C61C2411yescharacteristic
100C2×D4×C61—44no—
101C2×D4×C61—44no—
102C2×D4×C61—44no—
103C2×D4×C61—48no—
104C2×D4×C61—48no—
105C22×C4×C61—22no—
106C22×C4×C61—22no—
107C22×C4×C61—22no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—22no—
111C22×C4×C61—22no—
112C22×C4×C61—21no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—21no—
116C22×C4×C61—22no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61C2×Q812yes—
150C22×C4×C61#4114yes—
151C22×C4×C61#4114yes—
152C4⋊C4×C61—48no—
153C4⋊C4×C61—48no—
154C22⋊C4×C61—44no—
155C22⋊C4×C61—48no—
156C22⋊C4×C61—48no—
157C22⋊C4×C61—48no—
158C22⋊C4×C61—44no—
159C22⋊C4×C61—48no—
160C22⋊C4×C61—44no—
161C22⋊C4×C61—44no—
162C23×C61—22no—
163C23×C61—22no—
164C23×C61—22no—
165C23×C61—22no—
166C23×C61—22no—
167C23×C61—22no—
168C23×C61—24no—
169C23×C61—24no—
170C23×C61—24no—
171C23×C61—24no—
172C23×C61—42no—
173C23×C61—42no—
174C23×C61—42no—
175C23×C61—42no—
176C23×C61—42no—
177C23×C61—42no—
178C23×C61—42no—
179C23×C61—42no—
180C23×C61—42no—
181C23×C61—42no—
182C23×C61—42no—
183C23×C61—42no—
184C23×C61—41no—
185C23×C61—41no—
186C23×C61—42no—
187C23×C61—42no—
188C23×C61—42no—
189C23×C61—42no—
190C23×C61—41no—
191C23×C61—41no—
192C23×C61—41no—
193C23×C61—42no—
194C23×C61—42no—
195C23×C61—42no—
196C23×C61—42no—
197C23×C61—42no—
198C23×C61—41no—
199C23×C61—42no—
200C23×C61—42no—
201C23×C61—42no—
202C23×C61—41no—
203C23×C61—41no—
204C23×C61C22×Q811yescharacteristic
205C23×C61C2×#4112yes—
206C23×C61C2×#4112yes—
207C23×C61H(5,𝔽2)12yes—
208C23×C61H(5,𝔽2)12yes—
209C23×C61H(5,𝔽2)11yescharacteristic
210C23×C61H(5,𝔽2)12yes—
211C23×C61H(5,𝔽2)12yes—
212C23×C61H(5,𝔽2)11yescharacteristic
213D4×C61—416no—
214C2×C4×C61—24no—
215C2×C4×C61—24no—
216C2×C4×C61—24no—
217C2×C4×C61—24no—
218C2×C4×C61—22no—
219C2×C4×C61—22no—
220C2×C4×C61—22no—
221C2×C4×C61—24no—
222C2×C4×C61—24no—
223C2×C4×C61—42no—
224C2×C4×C61—42no—
225C2×C4×C61—42no—
226C2×C4×C61—42no—
227C2×C4×C61—42no—
228C2×C4×C61—42no—
229C2×C4×C61—42no—
230C2×C4×C61—42no—
231C2×C4×C61—42no—
232C2×C4×C61—42no—
233C2×C4×C61—42no—
234C2×C4×C61—42no—
235C2×C4×C61—42no—
236C2×C4×C61—42no—
237C2×C4×C61—42no—
238C2×C4×C61—42no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61—42no—
246C2×C4×C61—42no—
247C2×C4×C61—42no—
248C2×C4×C61—42no—
249C2×C4×C61—42no—
250C2×C4×C61—42no—
251C2×C4×C61—42no—
252C2×C4×C61—42no—
253C2×C4×C61—42no—
254C2×C4×C61—42no—
255C2×C4×C61—42no—
256C2×C4×C61—42no—
257C2×C4×C61—42no—
258C2×C4×C61—42no—
259C2×C4×C61—42no—
260C2×C4×C61—42no—
261#17272C6111yesmaximal, characteristic, direct product factor, Sylow
262C22×C61—42no—
263C22×C61—42no—
264C22×C61—42no—
265C22×C61—42no—
266C22×C61—44no—
267C22×C61—44no—
268C22×C61—44no—
269C22×C61—44no—
270C22×C61—42no—
271C22×C61—42no—
272C22×C61—82no—
273C22×C61—82no—
274C22×C61—82no—
275C22×C61—82no—
276C22×C61—82no—
277C22×C61—82no—
278C22×C61—82no—
279C22×C61—82no—
280C22×C61#53812yes—
281C22×C61#53812yes—
282C22×C61#53812yes—
283C22×C61#53812yes—
284C22×C61#54012yes—
285C22×C61#54012yes—
286C22×C61#54311yescharacteristic
287C22×C61#54311yescharacteristic
288C22×C61#54311yescharacteristic
289C22×C61#55111yescharacteristic
290C22×C61#55312yes—
291C22×C61#55412yes—
292C22×C61#55412yes—
293C22×C61#55512yes—
294C22×C61#55911yescharacteristic
295C22×C61#56011yescharacteristic
296C22×C61#56012yes—
297C22×C61#56012yes—
298C22×C61#56012yes—
299C22×C61#56012yes—
300C22×C61H(3,𝔽4)11yescharacteristic
301C4×C61—44no—
302C4×C61—42no—
303C4×C61—44no—
304C4×C61—82no—
305C4×C61—82no—
306C4×C61—82no—
307C4×C61—82no—
308#1443C2×C6112yescomplemented
309#1441C2×C6112yescomplemented
310#1439C2×C6112yescomplemented
311#1439C2×C6112yescomplemented
312#1439C2×C6112yescomplemented
313#1439C2×C6112yescomplemented
314#1438C2×C6111yescharacteristic
315#1438C2×C6111yescharacteristic
316#1438C2×C6111yescharacteristic
317C2×C61—82no—
318C2×C61—82no—
319C2×C61#274811yescharacteristic
320C2×C61#275612yes—
321C2×C61#278012yes—
322C2×C61#278412yes—
323C2×C61#280312yes—
324C2×C61#280411yescharacteristic
325C2×C61#282512yes—
326C2×C61#282812yes—
327C2×C61#284211yescharacteristic
328C23×D4C22×C6111yescharacteristic
329C22×C4⋊C4C22×C6112yes—
330C22×C4⋊C4C22×C6112yes—
331C22×C22⋊C4C22×C6111yescharacteristic
332C22×C22⋊C4C22×C6112yes—
333C22×C22⋊C4C22×C6112yes—
334C22×C22⋊C4C22×C6112yes—
335C22×C22⋊C4C22×C6111yescharacteristic
336C22×C22⋊C4C22×C6112yes—
337C22×C22⋊C4C22×C6111yescharacteristic
338C22×C22⋊C4C22×C6111yescharacteristic
339C2×#95C22×C6112yes—
340C2×#95C22×C6111yescharacteristic
341C2×#95C22×C6112yes—
342C2×#95C22×C6112yes—
343C2×#95C22×C6111yescharacteristic
344C2×#95C22×C6112yes—
345C2×#95C22×C6112yes—
346C2×#95C22×C6112yes—
347C2×#95C22×C6112yes—
348C2×#95C22×C6112yes—
349C61#1727211yescharacteristic, direct product factor, Sylow
350C25C23×C6111yescharacteristic
351C25C23×C6111yescharacteristic
352C22×D4—41no—
353C22×D4—42no—
354C22×D4—42no—
355C22×D4—41no—
356C22×D4Q8×C6114yes—
357C23×C4C23×C6112yes—
358C23×C4C23×C6112yes—
359C23×C4C23×C6112yes—
360C23×C4C23×C6112yes—
361C23×C4C23×C6111yescharacteristic
362C23×C4C23×C6112yes—
363C23×C4C23×C6112yes—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—41no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—41no—
383C2×C22⋊C4—41no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—41no—
390#95—24no—
391#95—42no—
392#95—42no—
393#95—42no—
394#95—42no—
395#95—41no—
396#95—41no—
397#95—42no—
398#95—42no—
399#95—42no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—21no—
412C24—21no—
413C24—22no—
414C24—21no—
415C24—21no—
416C24C2×Q8×C6112yes—
417C24C2×Q8×C6112yes—
418C24C24×C6111yescharacteristic
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—44no—
422C2×D4—48no—
423C2×D4—48no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4C2×Q8×C6112yes—
469C22×C4#41×C6114yes—
470C22×C4#41×C6114yes—
471C4⋊C4—48no—
472C4⋊C4—48no—
473C22⋊C4—44no—
474C22⋊C4—48no—
475C22⋊C4—48no—
476C22⋊C4—48no—
477C22⋊C4—48no—
478C22⋊C4—44no—
479C22⋊C4—44no—
480C22⋊C4—44no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—22no—
486C23—22no—
487C23—24no—
488C23—24no—
489C23—24no—
490C23—24no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—41no—
504C23—41no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—41no—
510C23—41no—
511C23—42no—
512C23—41no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23C22×Q8×C6111yescharacteristic
524C23C2×#41×C6112yes—
525C23C2×#41×C6112yes—
526C23H(5,𝔽2)×C6112yes—
527C23H(5,𝔽2)×C6112yes—
528C23H(5,𝔽2)×C6111yescharacteristic
529C23H(5,𝔽2)×C6112yes—
530C23H(5,𝔽2)×C6112yes—
531C23H(5,𝔽2)×C6111yescharacteristic
532D4—416no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C22—44no—
581C22—44no—
582C22—44no—
583C22—44no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—82no—
591C22—82no—
592C22—82no—
593C22—82no—
594C22—82no—
595C22—82no—
596C22—82no—
597C22—82no—
598C22C61×#53812yes—
599C22C61×#53812yes—
600C22C61×#53812yes—
601C22C61×#53812yes—
602C22C61×#54012yes—
603C22C61×#54012yes—
604C22C61×#54311yescharacteristic
605C22C61×#54311yescharacteristic
606C22C61×#54311yescharacteristic
607C22C61×#55111yescharacteristic
608C22C61×#55312yes—
609C22C61×#55412yes—
610C22C61×#55412yes—
611C22C61×#55512yes—
612C22C61×#55911yescharacteristic
613C22C61×#56012yes—
614C22C61×#56012yes—
615C22C61×#56012yes—
616C22C61×#56011yescharacteristic
617C22C61×#56012yes—
618C22C61×H(3,𝔽4)11yescharacteristic
619C4—44no—
620C4—42no—
621C4—44no—
622C4—82no—
623C4—82no—
624C4—82no—
625C4—82no—
626C2—82no—
627C2—82no—
628C2C61×#274811yescharacteristic
629C2C61×#275612yes—
630C2C61×#278012yes—
631C2C61×#278412yes—
632C2C61×#280312yes—
633C2C61×#280411yescharacteristic
634C2C61×#282512yes—
635C2C61×#282812yes—
636C2C61×#284211yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutator, Frattini, cosocleC24C24×C61
prime radicalC23×D4×C61C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C61×#1443C2semidirect
2. C61×#1441C2semidirect
3. C61×#1439C2semidirect
4. C61×#1439C2semidirect
5. C61×#1439C2semidirect
6. C61×#1439C2semidirect
261. #17272C61direct (N × H)
308. #1443C2×C61semidirect
309. #1441C2×C61semidirect
310. #1439C2×C61semidirect
311. #1439C2×C61semidirect
312. #1439C2×C61semidirect
313. #1439C2×C61semidirect
349. C61#17272direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C61×#14432
C61×#14412
C61×#14392
C61×#14382
#1727261